#### by Rob Kirby

James M. Kister was born on 29 June 1930 in Cleveland, Ohio to James Leonard Kister and Katherine Sherrick Kister. Jim’s paternal grandfather came to Ohio from Pennsylvania in 1840, found land with a stream; built a dam, waterwheel and mill; and then ground wheat and corn and made cider.

Jim’s father, JLK, did not finish high school, but had a talent with machinery. In 1908 his father bought a car in Chicago, which was then disassembled, boxed, and shipped by train to Millbrook, Ohio (named for the Kister mill). JLK and his father took a buggy to the train station where JLK reassembled the car and drove it home! (That seems an odd way to get a car from Chicago to Ohio, even in 1908.) JLK went on to work as an inspector of cars and trucks for White Motor Company (later bought by Mack) in Cleveland.

Jim lived in Cleveland through high school, winning prizes in math and physics. He went to Wooster College (Ohio) from 1948–52, winning the Rensselaer Prize in math. Melcher Fobes, a Hassler Whitney student at the time, was the main math teacher at Wooster, and encouraged Jim to go to Harvard for graduate work.

Jim started well at Harvard in 1952, but fell ill with a lung infection and had to leave Harvard before Thanksgiving and go to live in Tucson for its drier air. After a few months Los Alamos called with a job offer (George Birkhoff helped). Jim worked there for almost two years, with a three month break when the lower lobe of his left lung was removed.

On the advice of Stanislaw Ulam and C. J. Everett, and for the better air, Jim began graduate school at the University of Wisconsin in Madison in fall, 1955. That semester Jim took a point set topology course from Bob Williams (a Gordon Whyburn Ph.D. at the University of Virginia) and this got Jim interested in topology.

Jim met Sue Spence in summer 1955. They were married in 1956 and daughter Karen was born in December 1957. A Wisconsin fellowship only paid \$1500 so the young couple went to Los Alamos in summer 1956 to make extra money.

Ulam wanted Jim to join his team to work on a chess playing program.
This seemed too formidable so the chess board was shrunk to __\( 6 \times
6 \)__ and the rooks were eliminated. They wrote a program and got a good
chess player,
Martin Kruskal,
to test the program. Kruskal spotted
the program a queen, and then did not have an easy time beating it.
Jim gave a talk on the chess playing program before a large audience
at a meeting of the Association for Computing Machinery in Los
Angeles, and published a paper
[1].
A couple of courses from
R H Bing
in 1956–57 led to Bing becoming Jim’s
Ph.D. advisor. Bing was away at the Institute for Advanced Study in
1957–58 and when he returned he suggested that Jim work on the Side
Approximation Theorem (later proved by Bing
[e4]).
Instead Jim, in early 1959, saw that the space of bounded
homeomorphisms (with the compact-open topology) of __\( \mathbb{R}^n \)__ is
contractible, for any __\( n \)__. (Bounded means that there is some constant
__\( K \)__ such that the homeomorphism does not move any point more than
distance __\( K \)__.) The proof took one page, and can be seen as a canonical
version of the Alexander isotopy
[e1]
which shows
that a homeomorphism of the __\( n \)__-ball, __\( B^n \)__, which is equal to the
identity on the bounding __\( (n-1) \)__-sphere, is isotopic to the identity.
Jim saw that if one squeezes the homeomorphism of __\( \mathbb{R}^n \)__ into a
homeomorphism of __\( B^n \)__, then it will be equal to the identity on the
boundary. In his Math Review,
S. S. Cairns
called the proof
“remarkably efficient”, which it certainly is.

Bing reportedly asked the authorities whether the University would
accept a one page thesis for a Ph.D. The answer is unknown and
irrelevant for Jim also at the same time proved that the space of
homeomorphisms of a 3-manifold is locally connected
[2].
Jim put his bounded homeomorphisms theorem into
[2],
which had 3-manifolds in the title, but
no mention of higher dimensions. That led to my overlooking the
result for many decades, and led me to cite instead a paper of
Ed Connell
[e5]
in my paper
[e7]
using the torus trick
to prove local contractibility for all homeomorphisms (not just
bounded) of __\( \mathbb{R}^n \)__. Jim’s result is key to my theorem, and it’s
embarrassing that my acquaintances and I didn’t know of its existence!

In 1963 Jim proved a very important theorem, that a topological
manifold has a tangent bundle
[6].
Milnor had defined the notion of a *microbundle* and showed that
microbundles had many of the useful properties of actual bundles
[e6].
Jim showed that every microbundle (over a locally finite, finite
dimensional complex) contains a bundle (with fiber __\( \mathbb{R}^n \)__ and group
equal to the space of homeomorphisms of __\( \mathbb{R}^n \)__ with the compact open
topology). The key to the proof is the theorem stating that the space
of homeomorphisms of __\( \mathbb{R}^n \)__ is a weak deformation retract of the space
of embeddings of __\( \mathbb{R}^n \)__ into
__\( \mathbb{R}^n \)__.

Kervaire
called the proof, “elementary but delicate”, in his Math
Review, which is accurate but misses the fact that many geometric
proofs from that era looked elementary, but *only* after the fact.

If __\( T \)__ is a homeomorphism of period __\( r \)__ on Euclidean space __\( E^n \)__, then
P. A. Smith
[e2]
proved that __\( T \)__ has a fixed point if __\( r \)__ is prime or a prime power.
Then
Conner
and
Floyd
[e3]
gave examples when __\( r \)__ is not a prime power of contractible spaces with periodic maps with no fixed points.

Jim wrote two papers
[3]
[5]
giving counterexamples for all __\( r \)__ which are not prime powers. The
second paper constructs a map on a contractible infinite complex __\( K \)__
which is then embedded equivariantly in __\( E^n \)__ for __\( n > 7 \)__, and then a
regular neighborhood of __\( K \)__ is the desired Euclidean space. The map
can be made differentiable, and these examples are nearly best
possible, the only case left open was __\( n=7 \)__. The case __\( n=7 \)__ has been
settled:
R. Oliver
announced fixed point free maps in [*Notices of the AMS*,
**26** (1979), no. 2, A251], but details were never published. In
[e8]
the four authors give the relevant details of the __\( n=7 \)__ proof.

Jim and
Russ McMillan
constructed
[4]
a contractible open manifold __\( M \)__ which cannot be embedded in __\( E^3 \)__. All previous such examples were embeddable in __\( E^3 \)__. However, __\( M \times E^1 \)__ and __\( E^4 \)__ are combinatorially equivalent.

While on sabbatical at Oxford University in 1977, Jim met Jane Bridge, a mathematical logician, tenured at Somerville College of Oxford University. She was a student of Robin Gandy and thus a granddaughter of Alan Turing. Jane and Jim were married in 1978 and returned to Ann Arbor where Jane became an editor of Math Reviews. In 1998 she became the Executive Director of MR.

I met Jim in 1966–67 when he spent a year at UCLA. He gave a course on topological bundles and his notes from that course and my notes from a course two years later on triangulations of topological manifolds led us to plan a book together. Finishing this book kept getting put off — even though it is now 90% done. It should have been finished before Jim died, and will be soon.

Jim was a very good friend, a good athlete (despite being plagued by bronchiectasis all his life) and in particular was a cagey tennis player.